Why Do Causal Dynamical Triangulations Utilize a Partition Function?

[Schreiberdk]

I just want to ask why Causal Dynamical Triangulations use a partition function for describing the dynamics of the whole theory. Does the theory have some deep relation to statistical mechanics because of this formulation of the theory? Or is the partition function also a usual terminology to use in QFT?

 

[atyy]

QFT and classical statistical mechanics are related, so QFT sometimes uses stat mech terminology (partition function), just as stat mech sometimes uses QFT terminology (Feynman diagrams). This is due to Feynman's path integral in which quantum mechanics is a weighted sum over paths, just as statistical mechanics is a Boltzmann weighted sum over microstates.

http://arxiv.org/abs/hep-lat/9807028, p21-22

http://arxiv.org/abs/1009.5966 (example of QFT terminology in random processes)

 

[tom.stoer]

For quantum mechanics one can show that the so-called Wick rotation from t to it (i = imaginary unit) of the path integral is equivalent to a transformation to a partition function. The unitary time evolution of QM is replaced by a diffusion process.

The argument cannot be made rigorous in QFT but in CDT with a discrete PI it works rather nicely. For computational purposes (Monte-Carlo and importance sampling) the diffusion process is much more tractable due to the exponential damping exp(-S) instead of the oscillations coming from exp(iS).